Abstract
This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.
Highlights
The motor system uses stiffness modulation to maintain stability of the arm during interactions with the environment
We show how the systems’ equations are normalized with respect to the inertial matrix, and how the eigenvectors and the stiffness and damping parameters of a second order, two degree-of-freedom (DOF) system are computed through the implementation of our modal analysis
We have presented a new technique for estimating arm viscoelastic characteristics during both static postural and movement conditions
Summary
The motor system uses stiffness modulation to maintain stability of the arm during interactions with the environment. Stochastic methods are based on ensemble techniques [20,21,22,23] and even though they identify the system non-parametrically they require hundreds of perturbed repetitions of the same movement to obtain a reliable estimate of stiffness. These repetitions can induce muscle co-contraction that leads to stiffening of the arm joints [24], and can strongly reduce stretch reflexes [25]. A method that could estimate dynamic changes in arm stiffness on a trial-by-trial basis would constitute an ideal tool to monitor changes in stiffness over time
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